Primality proof for n = 9311:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=19.html>19 is prime.</a>
<br>b^((n-1)/19)-1 mod n = 4238, which is a unit, inverse 8720.
<p><a href=7.html>7 is prime.</a>
<br>b^((n-1)/7)-1 mod n = 763, which is a unit, inverse 8530.
<p>(7^2 * 19) divides n-1.
<p>(7^2 * 19)^2 > n.
<p>n is prime by Pocklington's theorem.